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Rudiy27
3 years ago
12

Day and Night Kennel charges $20 per day plus a one-time food fee of $15 to board a pet. Bark Time Hotel charges $30 per day plu

s a one-time food fee of $5. Which system represents this real-world situation?
Mathematics
1 answer:
BaLLatris [955]3 years ago
7 0

Answer:

See below.

Step-by-step explanation:

Let <em>x</em> represent the number of days.

Since Day and Night Kennel charges a fee of $20 per day and only a one-time fee of $15:

y=20x+15

Where <em>y</em> represents the total cost, <em>20x</em> represents the cost for staying <em>x</em> days and <em>15</em> is the initial one-time fee.

For Bark Time Hotel, similarly:

y=30x+5

Again, <em>y</em> represents the total cost, <em>30x</em> represents the cost for staying <em>x</em> days, and <em>5</em> is the initial one-time fee.

Thus, the system of equations is:

y=20x+15\\y=30x+5

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Answer:

Length=10.5\ ft

Width=10.5\ ft

Area=110.25\ ft^{2}

Step-by-step explanation:

Let

x----> the length of the rectangular garden

y---> the width of the rectangular garden

we know that

The perimeter of the rectangle is equal to

P=2(x+y)

we have

P=42\ ft

so

42=2(x+y)

simplify

21=(x+y)

y=21-x------> equation A

Remember that the area of rectangle is equal to

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substitute equation A in equation B

A=x(21-x)

A=21x-x^{2}----> this is a vertical parabola open downward

The vertex is a maximum

The y-coordinate of the vertex is the maximum area

The x-coordinate of the vertex is the length side of the rectangle that maximize the area

using a graphing tool

The vertex is the point (10.5,110.25)

see the attached figure

so

x=10.5\ ft

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y=21-10.5=10.5\ ft

The garden is a square

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The following are true.

(a)The width of the second  table is 2 feet.

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